How much time and risk is doing it this way worth?
I will argue that the presented approach is the "right thing" (reap what you sow) and increasing the search space is the "wrong thing" (why should US companies get more than their 5% of programming talent?).
I don't want US companies to have more talent than the US population can produce. I actually consider their requests stealing. It's not theirs to take. If they can't produce their own talent then they should perish by their own merits.
That being said, I don't believe in the 95/5% figure proposed by Graham. I think everybody can be a valuable partner given enough motivation.
I also think that they are not looking for talent but for slaves. It's really just imperialism in disguise.
You touch on why I don't like increased immigration, which is the stealing aspect. The problem is you take prospective entrepreneurs and great developers from other nations and slave them to US companies at threat of deportation. It is hard to be anything but a wage slave in that environment, which is exactly what companies want, and while the outside developers might have a grass is greener effect going on, is really not in their best interests. There are a lot of places to go if your home country is shit, and you can make a much better deal than an h1b.
Perhaps you feel the same way about labor movement within the US? Have you ever moved from one county, or one US state to another for educational or career opportunities? If someone was to move from Virginia to California, would that be a case of California 'stealing'from Virginia? I think it is, in the mechanical sense of virginia loses talent and taxes, and California gains it: surely what matters though, is that the right of humans to engage in the 'pursuit of happiness' should outweigh the right of a state (including nation states) to restrict such movement.
If you accept that idea, you can still argue that the obligations of a nation state are to promote the wellbeing of its own citizens above that of non citizens, but we shouldn't pretend that the barriers we put up are some noble effort to prevent 'stealing' from poor countries: people own the right to their lives and labor, not their state or government of origin.
However, two flaws with your suggestions: time and risk. Increasing the search space of people eliminates/reduces both of these.